A force applied on a body is represented as

\(\vec F = 2\hat i + 4\;\hat j + 4\;\hat k\)

And accelerated it at 2 m/s². The mass of the body is

Concept:

• Force exerted on an object is directly proportional to the mass of the object and the rate at which it is accelerated
• F = m × a
• And for converting vector quantity to its scalar quantity, it can be given as

\(F = \sqrt {{x^2} + {y^2} + {z^2}}\)

Here x, y, and z are a magnitude of vector r along X, Y, and Z-axis respectively.

Calculation:

Given that,

Accelerated (a) = 5 m/s²

\(\vec F = 2\hat i + 4\;\hat j + 4\;\hat k\)

Thus, the magnitude of force will be

\(F = \sqrt {{2^2} + {4^2} + {4^2}} = \sqrt {36} = 6\;N\)

Now the force is expressed as mass times acceleration,

i.e., F = m × a ⇒ m = F / a

\(\therefore m = \frac{{6\;N}}{{2\;m/{s^2}}} = 3\;kg\)